Convert all complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form.? $((2+2i)^5 (-3+i)^3) /(sqrt 3+i)^10$

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Answer 1 · 2018-05-14T11:40:23

$(27sqrt3)/4-i27/4$

So this took me so many attempts and here it goes:

Find the r values using this formula:

$r=sqrt (x^2+y^2)$

Plug in:

$([2sqrt2 (cos45^o + isin45^o)]^5[3sqrt2 (cos135^o + isin135^o)]^3 )/[2(cos 30^o + isin30^o)]^10$

Power and Multiply:

$(2sqrt2)^5$ see how I powered the $2sqrt2$ and you do the same with the rest

$((2sqrt2)^5(cos5 times 45^o + isin5 times45^o)(3sqrt2)^3(cos 3 times 135^o +isin3 times 135^o))/(2^10(cos10 times + isin10 times 30))$

Simplify:

$(128sqrt2(cos225^o + isin225^o) 54sqrt2(cos405^o + isin405^o))/(1024(cos 300^o + isin 300^o))$

$(13824 (cos630^o + isin630^o)) /(1024(cos300^o + isin300^o))$

Divide:

$27/2$ $(cos630^o-300^o + isin630^o-300^o)$

Simplify:

$27/2$ $(cos330^o + isin330^o)$

Which gives your answer . . .

Convert all complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form.? ((2+2i)^5 (-3+i)^3) /(sqrt 3+i)^10((2+2i)^5 (-3+i)^3) /(sqrt 3+i)^10